Intersection+2C-1

__Intersection__
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In order to find the point of intersection of two linear equations, it is helpful to have the equations of two lines in slope-intercept form.

Slope intercept form: **y = mx + b**. In order to find the point of intersection we need an X and Y coordinate. Once we find the X-coordinate, we can plug it into one of the equations and solve for Y.
 * m** is the slope
 * b** is the y-intercept.

y = 2x + 2 y = x + 1 ||  ||
 * **Example 1:** || **Explanation** ||
 * Where do these equations intersect?
 * 0= x + 1 || First we need to find the X coordinate. In order to do this we can subtract these two equations. Doing this eliminates 'y'. ||
 * -1 = x || Next we can subtract 1 from both sides to isolate the X. ||
 * x = -1 || Now we have our X-coordinate. ||
 * y = (-1) + 1 || Since we have the X we can now plug it into the original equation ( y = x + 1). ||
 * y = 0 || Now we have our Y-coordinate. ||
 * (-1,0) || Our intersection is (-1,0). ||

__Checking your solutions__
If you have the necessary resources and easier way of finding intersection is by graphing. You take your two equations and either put them both into a graphing calculator or graph them on paper. However, it is helpful to have your equation in slope-intercept form first (y = mx + b). If it is not you **should** put it in slope-intercept form before solving.

This [|link] is also a great help.

__Further Discussion__

 * Why are we allowed to subtract equations?